Instability of a planar fluid interface under a tangential electric field in a stagnation point flow

The interface between two immiscible fluids can become unstable under the effect of an imposed tangential electric field along with a stagnation point flow. This canonical situation, which arises in a wide range of electrohydrodynamic systems including at the equator of electrified droplets, can result in unstable interface deflections where the perturbed interface gets drawn along the extensional axis of the flow while experiencing strong charge build-up. Here, we present analytical and numerical analyses of the stability of a planar interface separating two immiscible fluid layers subject to a tangential electric field and a stagnation point flow. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic conduction, advection by the flow and finite charge relaxation. Using this model, we perform a local linear stability analysis in the vicinity of the stagnation point to study the behaviour of the system in terms of the relevant dimensionless groups of the problem. The local theory is complemented with a numerical normal-mode linear stability analysis based on the full system of equations and boundary conditions using the boundary element method. Our analysis demonstrates the subtle interplay of charge convection and conduction in the dynamics of the system, which oppose one another in the dominant unstable eigenmode. Finally, numerical simulations of the full nonlinear problem demonstrate how the coupling of flow and interfacial charge dynamics can give rise to nonlinear phenomena such as tip formation and the growth of charge density shocks.

An Improved Lattice Hydrodynamic Model by considering the Effect of “Backward-Looking” and Anticipation Behavior

In order to prevent the occurrence of traffic accidents, drivers always focus on the running conditions of the preceding and rear vehicles to change their driving behavior. By taking into the “backward-looking” effect and the driver’s anticipation effect of flux difference consideration at the same time, a novel two-lane lattice hydrodynamic model is proposed to reveal driving characteristics. The corresponding stability conditions are derived through a linear stability analysis. Then, the nonlinear theory is also applied to derive the mKdV equation describing traffic congestion near the critical point. Linear and nonlinear analyses of the proposed model show that how the “backward-looking” effect and the driver’s anticipation behavior comprehensively affect the traffic flow stability. The results show that the positive constant γ , the driver’s anticipation time τ , and the sensitivity coefficient p play significant roles in the improvement of traffic flow stability and the alleviation of the traffic congestion. Furthermore, the effectiveness of linear stability analysis and nonlinear analysis results is demonstrated by numerical simulations.

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Flows at moderate Reynolds numbers in inertial microfluidics enable high throughput and inertial focusing of particles and cells with relevance in biomedical applications. In the present work, we consider a viscosity-stratified three-layer flow in the inertial regime. We investigate the interfacial instability of a liquid sheet surrounded by a density-matched but more viscous fluid in a channel flow. We use linear stability analysis based on the Orr–Sommerfeld equation and direct numerical simulations with the lattice Boltzmann method (LBM) to perform an extensive parameter study. Our aim is to contribute to a controlled droplet production in inertial microfluidics. In the first part, on the linear stability analysis we show that the growth rate of the fastest growing mode $$\xi ^{*}$$ ξ ∗ increases with the Reynolds number $$\text {Re}$$ Re and that its wavelength $$\lambda ^{*}$$ λ ∗ is always smaller than the channel width w for sufficiently small interfacial tension $$\Gamma $$ Γ . For thin sheets we find the scaling relation $$\xi ^{*} \propto mt^{2.5}_{s}$$ ξ ∗ ∝ m t s 2.5 , where m is viscosity ratio and $$t_{s}$$ t s the sheet thickness. In contrast, for thicker sheets $$\xi ^{*}$$ ξ ∗ decreases with increasing $$t_s$$ t s or m due to the nearby channel walls. Examining the eigenvalue spectra, we identify Yih modes at the interface. In the second part on the LBM simulations, the thin liquid sheet develops two distinct dynamic states: waves traveling along the interface and breakup into droplets with bullet shape. For smaller flow rates and larger sheet thicknesses, we also observe ligament formation and the sheet eventually evolves irregularly. Our work gives some indication how droplet formation can be controlled with a suitable parameter set $$\{\lambda ,t_{s},m,\Gamma ,\text {Re}\}$$ { λ , t s , m , Γ , Re } . Graphical Abstract

Instability of Lenticular Vortices: Results from Laboratory Experiments, Linear Stability Analysis and Numerical Simulations

The instability of surface lenticular vortices is investigated using a comprehensive suite of laboratory experiments combined with numerical linear stability analysis as well as nonlinear numerical simulations in a two-layer Rotating Shallow Water model. The development of instabilities is discussed and compared between the different methods. The linear stability analysis allows for a clear description of the origin of the instability observed in both the laboratory experiments and numerical simulations. While global qualitative agreement is found, some discrepancies are observed and discussed. Our study highlights that the sensitivity of the instability outcome is related to the initial condition and the lower-layer flow. The inhibition or even suppression of some unstable modes may be explained in terms of the lower-layer potential vorticity profile.